从物理假设到经典和量子哈密顿和拉格朗日粒子力学
From physical assumptions to classical and quantum Hamiltonian and Lagrangian particle mechanics
摘要：
这项工作的目的是表明，粒子力学，无论是经典的和量子的，哈密顿量和拉格朗日量，可以从一些简单的物理假设。假设确定性和可逆的时间演化将给我们一个动力系统，其状态集形成一个拓扑空间，其演化规律是自同胚。假设系统是无穷小可约的-指定整个系统的状态和动力学等价于给出其无穷小部分的状态和动力学-将给我们一个经典的哈密顿系统。假设系统是不可约的-指定整个系统的状态和动力学告诉我们关于状态和它的子结构的动力学的任何信息-将给我们一个量子哈密顿系统。假设运动学等价，即研究轨迹等价于研究状态演化，将给我们拉格朗日力学，并将哈密顿量/拉格朗日量的形式限制为具有标量和矢量势的形式。
英文摘要：
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a dynamical system whose set of states forms a topological space and whose law of evolution is a self-homeomorphism. Assuming the system is infinitesimally reducible---specifying the state and the dynamics of the whole system is equivalent to giving the state and the dynamics of its infinitesimal parts---will give us a classical Hamiltonian system. Assuming the system is irreducible---specifying the state and the dynamics of the whole system tells us nothing about the state and the dynamics of its substructure---will give us a quantum Hamiltonian system. Assuming kinematic equivalence, that studying trajectories is equivalent to studying state evolution, will give us Lagrangian mechanics and limit the form of the Hamiltonian/Lagrangian to the one with scalar and vector potential forces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
